Lúcio Borges de Araújo

Validação cruzada com correção de autovalores e regressão isotônica nos modelos de efeitos principais aditivos e interação multiplicativa

This paper presents an application of AMMI models - Additive Main effects and Multiplicative Interaction model - for a thorough study about the effect of the interaction between genotype and environment in multi-environments experiments with balanced data. Two methods of crossed validation are presented and the improvement of these methods through the correction of eigenvalues, being these rearranged by the isotonic regression. A comparative study between these methods is made, with real data. The results show that the EASTMENT & KRZANOWSKI (1982) method selects a more parsimonious model and when this method is improved with the correction of the eigenvalues, the number of components are not modified. GABRIEL (2002) method selects a huge number of terms to hold back in the model, and when this method is improved by the correction of eigenvalue, the number of terms diminishes. Therefore, the improvement of these methods through the correction of eigenvalues brings a great benefit from the practical point of view for the analyst of data proceeding from multi-ambient, since the selection of numbers of multiplicative terms represents a profit of the number of blocks (or repetitions), when the model AMMI is used, instead of the complete model.

Multiattribute Response of Maize Genotypes Tested in Different Coastal Regions of Brazil

This work applies the three mode principal components analysis to analyze simultaneously the multiple attributes; to fit of models with additive main effects and multiplicative interaction effects (AMMI models) and the regressions models on sites (SREG models); to evaluate, respectively, the multivariate response of the genotype × environment interaction and the mean response of 36 genotypes of corn tested in 4 locations in Brazil. The results were presented by joint plots to identify the best genotypes for their adaptability and performance in the set of attributes.

Tucker3 method in biometrical research: Analysis of experiments with three factors, using R

The present work aims to propose a systematic study and interpretation of a variable response in relation to three factors, using a model of Joint Table Analysis, the Tucker3 model, as well as the joint biplot graph. The proposed method seems efficient and suitable for separating standard technical response, and the pattern of noise contained in a three inputs table, as well as allows its interpretation. The joint plot graph facilitates the study and interpretation of the data structure and provides additional information on these. In our application the aim is to identify the combinations of genotypes, locations and years that contribute or not to a high yield of bean cultivars.